Last Updated：2025/12/04

(algebra, field theory) A field K such that every irreducible polynomial over K has distinct roots.

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perfect field

Source Word

perfect field

(algebra, field theory) A field K such that every irreducible polynomial over K has distinct roots.

Japanese Meaning

代数学や体論において、既約多項式の全てが重複しない単純な根を持つ体

When studying separable extensions, it's useful to know whether a given perfect field admits any nontrivial purely inseparable extensions.

分離拡大を研究する際、与えられた完全体が非自明な純非分離拡大を持つかどうかを知っておくことは有用です。

Sense（1）

(algebra, field theory) A field K such that every irreducible polynomial over K has distinct roots.

If K is a perfect field of prime characteristic p, and if n is a nonnegative integer, then the mapping 𝛼→𝛼 from K to K is an automorphism.

perfect fields

（ plural ）